Blender Python: 3D Supershape
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### Summary

The 3D Supershape has been a favorite mathematical definition of mine. Supershapes offer a high level of formal variation. This Blender Python implementation follows previous versions I have created for The Proving Ground for platforms such as Grasshopper, Revit, and Processing.

### Code

```import bpy
import math

# mesh arrays
verts = []
faces = []
edges = []

#3D supershape parameters
m = 14.23
a = -0.06
b = 2.78
n1 = 0.5
n2 = -.48
n3 = 1.5

scale = 3

Unum = 50
Vnum = 50

Uinc = math.pi / (Unum/2)
Vinc = (math.pi/2)/(Vnum/2)

#fill verts array
theta = -math.pi
for i in range (0, Unum + 1):
phi = -math.pi/2
r1 = 1/(((abs(math.cos(m*theta/4)/a))**n2+(abs(math.sin(m*theta/4)/b))**n3)**n1)
for j in range(0,Vnum + 1):
r2 = 1/(((abs(math.cos(m*phi/4)/a))**n2+(abs(math.sin(m*phi/4)/b))**n3)**n1)
x = scale * (r1 * math.cos(theta) * r2 * math.cos(phi))
y = scale * (r1 * math.sin(theta) * r2 * math.cos(phi))
z = scale * (r2 * math.sin(phi))

vert = (x,y,z)
verts.append(vert)
#increment phi
phi = phi + Vinc
#increment theta
theta = theta + Uinc

#fill faces array
count = 0
for i in range (0, (Vnum + 1) *(Unum)):
if count < Vnum:
A = i
B = i+1
C = (i+(Vnum+1))+1
D = (i+(Vnum+1))

face = (A,B,C,D)
faces.append(face)

count = count + 1
else:
count = 0

#create mesh and object
mymesh = bpy.data.meshes.new("supershape")
myobject = bpy.data.objects.new("supershape",mymesh)

#set mesh location
myobject.location = bpy.context.scene.cursor_location
bpy.context.scene.objects.link(myobject)

#create mesh from python data
mymesh.from_pydata(verts,edges,faces)
mymesh.update(calc_edges=True)

#set the object to edit mode
bpy.context.scene.objects.active = myobject
bpy.ops.object.mode_set(mode='EDIT')

# remove duplicate vertices
bpy.ops.mesh.remove_doubles()

# recalculate normals
bpy.ops.mesh.normals_make_consistent(inside=False)
bpy.ops.object.mode_set(mode='OBJECT')

# subdivide modifier
myobject.modifiers.new("subd", type='SUBSURF')
myobject.modifiers['subd'].levels = 3

# show mesh as smooth
mypolys = mymesh.polygons
for p in mypolys:
p.use_smooth = True
```

### Different Parameters

```#3D supershape parameters
m = 14.13
a = -0.06
b = 2.78
n1 = -2
n2 = -.1
n3 = 1

scale = 3

Unum = 70
Vnum = 70

Uinc = math.pi / (Unum/2)
Vinc = (math.pi/2)/(Vnum/2)

#fill verts array
theta = -math.pi
for i in range (0, Unum + 1):
phi = -math.pi/2
r1 = 1/(((abs(math.cos(m*theta/4)/a))**n2+(abs(math.sin(m*theta/4)/b))**n3)**n1)
for j in range(0,Vnum + 1):
r2 = 1/(((abs(math.cos(m*phi/4)/a))**n2+(abs(math.sin(m*phi/4)/b))**n3)**n1)
x = scale * (r1 * math.cos(theta) * r2 * math.cos(phi))
y = scale * (r1 * math.sin(theta) * r2 * math.cos(phi))
z = scale * (r2 * math.sin(phi))

vert = (x,y,z)
verts.append(vert)
#increment phi
phi = phi + Vinc
#increment theta
theta = theta + Uinc
```
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